1916 americanpracnavi00bowdrich

8/6/2019 1916 americanpracnavi00bowdrich

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See typed listof tables inside this cover


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1916, 1930, 1951, 1934, and 1956 editions of(tables in back of book)

(1916) fable So. litle% Traverse table, degrees

Conversion of departure into differ-531

621634

755772

817

55B

4244

45

not in these editions - refer to1958 edition, Table 4, pace 106)

Meridional partsDistance of an object by tso bear

ings, degreestables

(not in these editions - refer to1988 edition, Table l?JLj^ise_140>Logarittes of numbersLogarithms of trigonometric func

tions, degreesLogarithmic and natural haversines

i


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No. 9

American Practical NavigatorAn Epitome of Navigation and

Nautical Astronomy

ORIGINALLY BYNATHANIEL BOWDITCH, LL. D.

PUBLISHED BY THEUNITED STATES HYDROGRAPHIC OFFICE

UNDER THE AUTHORITY OFTHE SECRETARY OF THE NAVY

WASHINGTONGOVERNMENT PRINTING OFFICE1916


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r

TEXT AND APPENDICES.

.300861


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NOTE ON REPRINT OF 1916. This reprint is the same as the 1914 edition, exceptthat the examples worked out in the text have been brought up to date to accord withthe form of the American Nautical Almanac as now published.


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CONTENTS OF F^RT I.Page.

AbbreviationsChapter I. Definitions relating to Navigation 9

II. Instruments and Accessories in Navigation 11III. The Compass Error 36IV. Piloting 56V. The Sailings 72

VI. Dead Reckoning 84VII. Definitions relating to Nautical Astronomy 87

VIII. Instruments employed in Nautical Astronomy 91IX. Time and the Nautical Almanac 102X. Correction of Observed Altitudes 115XI. The Chronometer Error 121XII. Latitude 126XIII. Longitude 140XIV. Azimuth 144XV. The Sumner Line 150XVI. The Practice of Navigation at Sea 169XVII. Marine Surveying 189XVIII. Winds 206XIX. Cyclonic Storms 212XX. Tides 225XXI. Ocean Currents 232XXII. Ice and its Movements in the North Atlantic Ocean 238

Appendix I. Extracts from the American Ephemeris and Nautical Almanac for the year 1916which have reference to examples for that year given in this work 248II. A collection of Forms for working Dead Reckoning and various Astronomical Sights,with notes explaining their application under all circumstances 254

III. Explanation of certain Rules and Principles of Mathematics of use in the Solutionof Problems in Navigation 266

IV. Maritime Positions and Tidal Data ; 278Index.. 358


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ABBREVIATIONS USED IN THIS WORK.Alt. (or ft) Altitude.a. m Ante meridian.Amp Amplitude.App Apparent.App. t Apparent time.Ast Astronomical.Ast. t Astronomical time.Aug Augmentation.Az. (orZ) Azimuth.C Course.C. C Chronometer correction.C W Chronometer minus watch.Chro. t Chronometer time.Co. L Co. latitude.Col Column.Corr Correction.Cos Cosine.Cosec Cosecant.Cot Cotangent.d (or Dec.) Declination.D (or D.Lo) Difference longitude.Dep Departure.Dev Deviation.Diff Difference.Dist Distance.DL Difference latitude.D. R Dead reckoning.E., Ely East, easterly.Elap. t Elapsed time.Eq. t Equation of time.F Longitude factor./ Latitude factor.G. (or Gr.) Greenwich.G. A. T Greenwich apparent time.G. M. T Greenwich mean time.G. S. T Greenwich sidereal time.ft Altitude.H Meridian altitude.H. A. (or t) Hour angle.Hav Haversine.H. D Hourly difference.H. P. (or Hor. par.). .Horizontal parallax.Hr-s Hour-s.H. W High water.I. C Index correction.L. (or Lat.) Latitude.L. A. T Local apparent time.L. M. T Local mean time.

L. S. T Local sidereal time.Lo. (or Long.) Longitude.Log Logarithm.Lun. Int Lunitidal interval.L. W Low water.A Longitude.m Meridional difference.Merid Meridian or noon.Mag Magnetic.M. D Minute s difference.Mid Middle.Mid. L Middle latitude.M. T Meantime.nat Natural.N., Nly North, northerly.N. A. (orNaut. Aim.) Nautical Almanac.Np Neap .Obs Observation.p (or P. D.) Polar distance.p. c Per compass.JP. D. (or p) Polar distance.P. L. (or Prop. Log.). Proportional logarithm.p. m Post meridian.p, & r Parallax and refraction.rar Parallax.R. A Right ascension.R. A. M. S Right ascension mean sun.Red Reduction.Ref Refraction.S., Sly South, southerly.S. D Semidiameter.Sec Secant.Sid Sidereal.Sin Sine.Spg Spring.t Hour angle.T Time.Tab Table.Tan Tangent.Tr. (or Trans. ) Transit.Var Variation.Vert Vertex or vertical.W., Wly West, westerly.W. T Watch time.z Zenith distance.Z Azimuth.6 Auxiliary angle.X Difference longitude in time.

SYMBOLS.The Sun.The Moon.* _ A Star or Planet.

"Q (C Alt. upper limb.LQ ([_ Alt. lower limb.(J) |3 Azimuthal angle.

A a ..Alpha./? ..Beta.F Y ..Gamma.Ad.. Delta.E e . .Epsilon.Z C -.Zeta.Hr) ..Eta.8 d ..Theta.

Iota.Kappa.Lambda.

u.

GREEK LETTERS.

f.K KA XM it

Degrees.Minutes of Arc.Seconds of Arc.Hours.Minutes of Time.Seconds of Time.

N v Nu.s e xi.o Omicron.n 7i Pi.

,P p Rho.1 a (r)... Sigma.T T Tau.T y Upsilon.

Phi.X x Chi.

Psi.Q a> Omega .


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CHAPTER I.DEFINITIONS KELATING TO NAVIGATION,

1. That science, generally termed Navigation, which affords the knowledgenecessary to conduct a ship from point to point upon the earth, enabling the marinerto determine, with a sufficient degree of accuracy, the position of his vessel at anytune, is properly divided into two branches : Navigation and Nautical Astronomy.2. Navigation, in its limited sense, is that branch which treats of the determination of the position of the ship by reference to the earth, or to objects thereon. Itcomprises (a) Piloting, in which the position is ascertained from visible objectsupon the earth, or from soundings of the depth of the sea, and (b) Dead Reckoning,in which the position at any moment is deduced from the direction and amount ofa vessel s progress from a known point of departure.3. Nautical Astronomy is that branch of the science which treats of the determination of the vessel s place by the aid of celestial objects the sun, moon, planets,or stars.

4. Navigation and Nautical Astronomy have been respectively termed Geo-Navigation and Celo-Navigation, to indicate the processes upon which they depend.5. As the method of piloting can not be employed excepting near land or inmoderate depths of water, the navigator at seamust fix his position either by dead reckoning or byobservation of celestial objects; the latter method ismore exact, but as it is not always available, theformer must often be depended upon.6. THE EARTH. The Earth is an oblatespheroid, being a nearly spherical, body slightlyflattened at the poles; its longer or equatorialaxis measures about 7,927 statute miles, and its Eshorter axis, around which it rotates, about 7,900statute miles.The Earth (assumed for purposes of illustration to be a sphere) is represented in figure 1.The Axis of Rotation, usually spoken of simplyas the Axis, is PP .The Poles are the points, P and P , in whichthe axis intersects the surface, and are designated,respectively, as the North Pole and the South Pole.The Equator is the great circle EQMW, formed by the intersection with theearth s surface of a plane perpendicular to the axis ; the equator is equidistant fromthe poles, every point upon it being^90 from each pole.Meridians are the great circles rQP , PMP , PM P , formed by the intersectionwith the earth s surface of planes secondary to the equator (that is, passing throughits poles and therefore perpendicular to its plane).Parallels of Latitude are small circles NTn, N n T , formed by the intersectionwith the earth s surface of planes passed parallel to the equator.The Latitude of a place on the surface of the earth is the arc of the meridianintercepted between the equator and that place. Latitude is reckoned North andSouth, from the equator as an origin, through 90 to the poles; thus, the latitudeof the point T is MT, north, and of the point T , MT, north. The Difference ofLatitude between any two places is the arc of a meridian intercepted between theirparallels of latitude, and is called North or South, according to direction; tnus, thedifference of latitude between T and T is Tn f or T n, north from T or south from T .The Longitude of a place on the surface of the earth is the arc of the equator intercepted between its meridian and that of some place from which the longitude is

9

FIG. l.


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10 ... fc .. DEFINITION RELATING TO NAVIGATION.reckoned. Longitude is measured East or West through 180 from the meridian ofa designated- place, such meridian being termed the Prime Meridian; the primemeridian used by most nations, including the United States, is that of Greenwich,England. If, in the figure, the prime meridian be PGQP , then the longitude of thepoint T is QM, east, and of T , QM , east. The Difference of Longitude between anytwo places is the arc of the equator intercepted between their meridians, and is calledEast or West, according to direction ; thus, the difference of longitude between T andT is MM , east from M or west from M . The Departure is the linear distance,measured on a parallel of latitude, between two meridians; unlike the various quantities previously defined, departure is reckoned in miles; the departure between twomeridians varies with the parallel of latitude upon which it is measured; thus, thedeparture between the meridians of T and T is the number of miles correspondingto the distance Tn in the latitude of T, or to n T in the latitude of T .The curved line which joins any two places on the earth s surface, cutting all themeridians at the same angle, is called the Rhumb Line, Loxodromic Curve, or Equiangular Spiral. In the figure this line is represented by TYT . The constant anglewhich this line makes with the meridians is called the Course; and the length of theline between any two places is called the Distance between those places;The unit of linear measure employed by navigators is the Nautical or Sea Mile,or Knot. This unit is defined in the United States of America as being 6,080.27feet in length and equal to one-sixtieth part of a degree of a great circle ot a spherewhose surface is equal in area to the area of the surface of the earth.The nautical mile is not exactly the same in all countries, but, from the navigator s standpoint, the various lengths adopted do not differ materially.

Since, upon the ocean, latitude has been capable of easier and more accuratedetermination than longitude, it might naturally be expected that there exists anintimate fixed relation between the nautical mile and the minute of latitude (or thelength of that portion of a meridian which subtends at the earth s center the angularmeasure of one minute); but on account of the fact that the earth is not a perfectsphere, a fixed relation does not exist, and the arc of a meridian that subtends anangle of 1 at the center of the earth varies slightly in length from the Equator tothe poles, being 6,045.95 feet at the Equator and 6,107.85 feet at the poles. Itsaverage length is 1,852.201 meters, or 6,076.82 feet. Accordingly in France,Germany, and Austria the nautical mile is 1,852 meters, 2,025.41 yards, or 6,076.23feet.For purposes of navigation the nautical mile is assumed to be equal to a minuteof latitude in all parts of the world; and, hence, when a vessel changes her positionto the north or south by 1 nautical mile, it may always be considered that the latitudehas changed 1 . Owing to the fact that the meridians converge toward the poles,the difference of longitude produced by a change of position ol 1 mile to the eastor west will vary with the latitude ; thus, a departure of 1 mile will equal a difference oflongitude of 1 at the Equator, but of more than 1 at any higherlatitude, being infact equal to I .l of longitude in latitude 30 and to 2 of longitude in latitude 60.In England the nautical mile, corresponding to the Admiralty knot, is regardedas having a length of 6,080 feet.The statute mile of 5,280 feet, which is employed in land measurements, iscommonly used in navigating river and lake vessels. This is notably the case on theGreat Lakes of America, but with the recognition of the advantages to be gamed bythe nractice of nautical astronomy in the navigation of these vessels, the use of thenautical mile is extending.The Great Circle Track or Course between any two places is the route betweenthose places along the circumference of the great circle which joins them. In thefigure this line is represented byT/T . From the properties of a great circle (which is acircle upon the earth s surface formed by the intersection of a plane passed throughits center) the distance between two points measured on a great circle track is shorterthan the distance upon any other line which joins them. Except when the twopoints are on the same meridian or when both lie upon the equator, the great circletrack will always differ from the rhumb line, and the great circle track wul intersecteach intervening meridian at a different angle.


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CHAPTER II.INSTRUMENTS AND ACCESSORIES IN NAVIGATION,DIVIDERS OB COMPASSES.

7. This instrument consists of two legs movable about a joint, so that thepoints at the extremities of the legs may be set at any required distance from eachother. It is used to take and transfer distances and to describe arcs and circles.When used for the former purpose it is termed dividers, and the extremities of bothlegs are metal points; when used for describing arcs or circles, it is called a compass,and one of the metal points is replaced by a pencil or pen.

PARALLEL RULERS.8. Parallel rulers are used for drawing lines parallel to each other in any direc

tion, and are particularly useful in transferring the rhumb-line on the chart to thenearest compass-rose to ascertain the course, or to lay off bearings and courses.PROTRACTOR.

9. This is an instrument used for the measurement of angles upon paper;there is a wide variation in the material, size, and shape in which it may be made.(For a description of the Three Armed Protractor, see art. 428, Chap. XVII.)THE CHIP LOG.

10. This instrument, for measuring the rate of sailing, consists of three parts;viz, the log-chip, the log-line, and the log-glass. A light substance thrown from theship ceases to partake of the motion 01 the vessel as soon as it strikes the water,and will be left behind on the surface; after a certain interval, if the distance of theship from this stationary object be measured, the approximate rate of sailing willbe given. The log-chip is the float, the log-line is the measure of the distance, andthe log-glass defines the interval of tune.The log-chip is a thin wooden quadrant of about 5 inches radius, loaded withlead on the circular edge sufficiently to make it float upright in the water. Thereis a hole in each corner of the log-chip, and the log-line is knotted in the one at theapex; at about 8 inches from the end there is seized a wooden socket; a piece ofline of proper length, being knotted in the other holes, has seized into its bight awooden peg to fit snugly into the socket before the log-chip is thrown; as soon asthe line is checked this peg pulls out, thus allowing the log-chip to be hauled inwith the least resistance.The log-line is about 150 fathoms in length, one end made fast to the log-chip,the other to a reel upon which it is wound. At a distance of from 15 to 20 fathomsfrom the log-chip a permanent mark of red bunting about 6 inches long is placedto allow sufficient stray line for the log-chip to clear the vessel s eddy or wake. Therest of the fine is divided into lengths of 47 feet 3 inches called Jcnots, by pieces offish-fine thrust through the strands, with one, two, three, etc., knots, according tothe number from stray-fine mark; each knot is further subdivided into five equallengths of two-tenths of a knot each, marked by pieces of white rag.The length of a knot depends upon the number of seconds which the log-glassmeasures; the length of each knot must bear the same ratio to the nautical mile(-gV of a degree of a great circle of the earth, or 6,080 feet) that the time of the glassdoes to an hour.

11


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12 INSTRUMENTS AND ACCESSORIES IN NAVIGATION.In the United States Navy all log-lines are marked for log-glasses of 28 seconds,for which the proportion is : 3600 : 6080 = 28s : x,

x being the length of the knot.Hence, z = 47ft.29, or47ft 3in .The speed of the ship is estimated in knots and tenths of a knot.The log-glass is a sand glass of the same shape and construction as the old hour

glass. Two glasses are used, one of 28 seconds and one of 14 seconds; the latter isemployed when the ship is going at a high rate of speed, the number of knots indicated on a line marked for a 28-second glass being doubled to obtain the true rateof speed.11. The log in all its parts should be frequently examined and adjusted; theEeg must be found to fit sufficiently tight

to keep the log-chip upright; the log-ne shrinks and stretches and should often be verified; the log-glass should becompared with a watch. One end of the glass is stopped with a cork, by removingwhich the sand may be dried or its quantity corrected.12. A ground log consists of an ordinary log-line, with a lead attached insteadof a chip; in shoal water, where there are no well-defined objects available for fixingthe position of the vessel and the course and speed are influenced by a tidal or othercurrent, this log is sometimes used, its advantage being that the lead marks a stationary point to which motion may be referred, whereas the chip would drift withthe stream. The speed, which is marked in the usual manner, is the speed overthe ground, and the trend of the line gives the course actually made good by thevessel. THE PATENT LOG.

13. This is a mechanical contrivance for registering the distance actually runby a vessel through the water. There are various types of patent logs, but for themost part they act upon the same principle, consisting of a registering device, a flyor rotator, and a log or towline; the rotator is a small spino3e with a number ofblades extending radially in such manner as to form a spiral, and, when drawn throughthe water in the direction of its axis, rotates about that axis after the manner of ascrew propeller; the rotator is towed from the vessel by means of a log or towlinefrom 30 to 100 fathoms in length, made fast at its apex, the line being of specialmake, so that the turns of the rotator are transmitted through it to. the worm shaftof the register, to which the inboard end of the line is attached; the registeringdevice is so constructed as to show upon a dial face the distance run, according tothe number of turns of its worm shaft due to the motion of the rotator; the registeris carried at some convenient point on the vessel s quarter; it is frequently foundexpedient to rig it out upon a small boom, so that the rotator will be towed clearof the wake.

14. Though not a perfect instrument, the patent log affords a means of determining the vessel s speed through the water. It will usually be found that theindications of the log are in error by a constant percentage, and the amount of thiserror should be determined by careful experiment and applied to all readings.Various causes may operate to produce inaccuracy of working in the patentlog, such as the bending of the blades of the rotator by accidental blows, fouling ofthe rotator by seaweed or refuse from the ship, or mechanical wear of parts of theregister. The length of the towline has much to do with the working of the log,and by varying the length the indications of the instrument may sometimes beadjusted when the percentage of error is small; it is particularly important that theline shall not be too short. The readings of the patent log can not be depended uponfor accuracy at low speeds, when the rotator does not tow horizontally, nor in a heador a following sea, when the effect depends upon the wave motion as well as uponthe speed of the vessel.15. Electrical registers for patent logs are in use, the distance recorded by themechanical register being communicated electrically to some point of the vesselwhich is most convenient for the purposes of those charged with the navigation.


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INSTRUMENTS AND ACCESSORIES IN NAVIGATION. 13

17 fathoms from the lead, same as at 7 fathoms.20 fathoms from the lead, with 2 knots.25 fathoms from the lead, with 1 knot.30 fathoms from the lead, with 3 knots.35 fathoms from the lead, with 1 knot.40 fathoms from the lead, with 4 knots.And so on.

16. A number of instruments based upon different physical principles havebeen devised for recording the speed of a vessel through the water and have beenused with varying degrees of success. Of these the hydraulic speed indicator, knownas the Nicholson Ship Log, affords an instance.17. The revolutions of the screw propeller afford in a steamer the most valuablemeans of determining a vessel s speed through the water. The number of revolutions per knot must be carefully determined for the vessel by experiment undervarying conditions of speed, draft, and foulness of bottom.

THE LEAD.18. This device, for ascertaining the depth of water, consists essentially of a

suitably marked line, having a lead attached to one of its ends. It is an invaluableaid to the navigator in shallow water, particularly in thick or foggy weather, and isoften of service when the vessel is out of sight of land.Two leads are used for soundings the Tiand-lead, weighing from 7 to 14 pounds,with a line marked to about 25 fathoms, and the deep-sea lead, weighing from 30 to100 pounds, the line being 100 fathoms or upward in length.Lines are generally marked as follows :2 fathoms from the lead, with 2 strips of leather.3 fathoms from the lead, with 3 strips of leather.5 fathoms from the lead, with a white rag.7 fathoms from the lead, with a red rag.10 fathoms from the lead, with leather having ahole in it.13 fathoms from the lead, same as at 3 fathoms.15 fathoms from the lead, same as at 5 fathoms.

Fathoms which correspond with the depths marked are called marks; the intermediate fathoms are called deeps; the only fractions of a fathom used are a halfand a quarter.A practice sometimes followed is to mark the hand-lead line in feet around thecritical depths of the vessel by which it is to be used.Lead lines should be measured frequently while wet and the correctness of themarking verified. The distance from the leadsman s hand to the water s edge shouldbe ascertained in order that proper allowance may be made therefor in takingsoundings at night.19. The deep-sea lead may be armed by filling with tallow a hole hollowed outin its lower end, by which means a sample of the bottom is brought up.

THE SOUNDING MACHINE.20. This machine possesses advantages over the deep-sea lead, for which it isa substitute, in that soundings may be obtained at great depths and with rapidityand accuracy without stopping the ship. It consists essentially of a stand holdinga reel upon which is wound the sounding wire, and which is controlled by a suitablebrake. Crank handles are provided for reeling in the wire after the sounding hasbeen taken. Attached to the outer end of the wire is the lead, which has a cavityat its lower end for the reception of the tallow for arming. Above the lead is a

cylindrical case containing the depth-registering mechanism; various devices are inuse for this purpose, all depending, however, upon the increasing pressure of thewater with increasing depths.21. In the Lord Kelvin machine a slender glass tube is used, sealed at one endand open at the other, and coated inside with a chemical substance which changescolor upon contact with sea water; this tube is placed, closed end up, in the metalcylinder; as it sinks the water rises in the tube, the contained air being compressedwith a force dependent upon the depth. The limit of discoloration is marked by aclearly defined line, and the depth of the sounoling corresponding to this line is readoff from a scale. Tubes that have been used in comparatively shallow water maybe used again where the water is known to be deeper.22. A tube whose inner surface is ground has been substituted for the chemical-coated lube, ground glass, when wet, showing clear. The advantage of these tubes


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14 INSTRUMENTS AND ACCESSORIES IN NAVIGATION.is that they may be used an indefinite number of times if thoroughly dried. Tofacilitate drying, a rubber cap is fitted to the upper end, which, when removed,admits of a circulation of the air through the tube.23. As a substitute for the glass tubes a mechanical depth recorder contained in asuitable case has been used. In this device the pressure of the water acts upon apiston against the tension of a spring. A scale with an index pointer records thedepth reached. The index pointer must be set at zero before each sounding.24. Since the action of the sounding machine, when glass tubes are used,depends upon the compression of the air, the barometric pressure of the atmospheremust be taken into account when accurate results are required. The correctionconsists in increasing the indicated depth by a fractional amount according to thefollowing table :

THE MARINER S COMPASS.25. The Mariner s Compass is an instrument consisting either of a singlemagnet, or, more usually, of a group of magnets, which, being attached to a graduated

circle pivoted at the center and allowed to swing freely in a horizontal plane, has atendency, when not affected by disturbing magnetic features within the ship, to liewith its magnetic axis in the plane of the earth s magnetic meridian, thus affording ameans of determining the azimuth, or horizontal angular distance from that meridian,of the ship s course and of all visible objects, terrestrial or celestial.26. The circular card of the compass is divided on its periphery into 360,frequently numbered from at North and South to 90 at East and West; alsointo thirty-two divisions of 11J each, called points, the latter being further dividedinto naif-points and quarter-points; still finer subdivisions, eighth-points, are some-tunes used, though not indicated on the card. A system of numbering the degreesfrom to 360, always increasing toward the right, is shown in figure 2. Thissystem is in use in the United States Navy and by the mariners of some foreignnations, and its general adoption would carry with it certain undoubted advantages.

27. Boxing the Compass is the process of naming the points in their order, and isone of the first things to be learned by the young mariner. The four principal pointsare called cardinal points and are named North, South, East, and West; each differsin direction from the adjacent one by 90, or 8 points. Midway between the cardinalpoints, at an angular distance of 45, or 4 points, are the inter-cardinal points, namedaccording to their position Northeast, Southeast, etc. Midway between eachcardinal and inter-cardinal point, at an angular distance of 22, or 2 points, is apoint whose name is made up of a combination of that of the cardinal with that ofthe inter-cardinal point: North-Northeast, East-Northeast, East-Southeast, etc. Atan angular distance of 1 point, or 11J, from each cardinal and inter-cardinal point(and therefore midway between it and the 22-division last described), is a pointwhich bears the name of that cardinal or inter-cardinal point joined by the word byto that of the cardinal point in the direction of which it lies : North by East, Northeastby North, Northeast by East, etc.


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INSTRUMENTS AND ACCESSORIES IN NAVIGATION. 15In boxing by fractional points, it is evident that each division may be referred toeither of the whole points to which it is adjacent; for instance, NE. by N. N. andNNE. E. would describe the same division. It is the custom in the United States

Navy to box from North and South toward East and West, excepting that divisionsadjacent to a cardinal or inter-cardinal point are always referred to that point; as

No. 1742JUNE 1908

FIG. 2.

N. i E., N. by E. E., NNE. $ E., NE. N., etc. Some mariners, however, make it apractice to box from each cardinal and inter-cardinal point toward a 22J-point (NNE.,ENE., etc.); as N. * E., N. by E. J E., NE. by N. * N., NE. i N., etc.The names of the whole points, together with fractional points (according to thenomenclature of the United States Navy), are given in the following table, which


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16 INSTRUMENTS AND ACCESSORIES IN NAVIGATION.shows also the degrees, minutes, and seconds from North or South to which eachdivision corresponds:


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INSTRUMENTS AND ACCESSORIES IN NAVIGATION. 1728. The compass card is mounted in a bowl which is carried in gimbals, thus

enabling the card to retain a horizontal position while the ship is pitching and rolling.A vertical black line called the lubber s line is marked on the inner surface of the bowl,and the compass is so mounted that a line joining its pivot with the lubber s fine isparallel to the keel line of the vessel; thus the lubber s line always indicates the compass direction of the ship s head.

29. According to the purpose which it is designed to fulfill, a compass is designated as a Standard, Steering, Check, or Boat Compass. On United States naval vessels additional compasses are designated as follows: Maneuvering, battle, auxiliarybattle, top, and conning-tower compasses.30. There are two types of magnetic compass in use, the liquid or wet and thedry; in the former the bowl is filled with liquid, the card being thus partially buoyedwith consequent increased ease of working on the pivot, and the liquid further servingto decrease the vibrations of the card when deflected by reason 01 the motion of thevessel or other cause. On account of its advantages the liquid compass is used inthe United States Navy.31. THE NAVY SERVICE T^-INCH LIQUID COMPASS. This consists of a skeletoncard 7i inches in diameter, made of tinned brass, resting on a pivot in liquid, withprovisions for two pairs of magnets symmetrically placed.The magnet system of the card consists of four cylindrical bundles of steel wires;these wires are laid side by side and magnetized as a bundle between the poles of apowerful electro-magnet. They are afterwards placed in a cylindrical case, sealed,and secured to the card. Steel wires made up into a bundle were adopted becausethey are more homogeneous, can be more perfectly tempered, and for the same weightgive greater magnetic power than a solid steel bar.Two of the magnets are placed parallel to the north and south diameter of thecard, and on the chords of 15 (nearly) of a circle passing through their extremities.These magnets penetrate the air vessel, to which they are soldered, and are furthersecured to the bottom of the ring of the card. The other two magnets of the systemare placed parallel to the longer magnets on the chords of 45 (nearly) of a circlepassing through their extremities and are secured to the bottom of the ring of the card.The card is of a curved annular type, the outer ring being convex on the upperand inner side, and is graduated to read to one-quarter point, a card circle beingadjusted to its outer edge and divided to half degrees, with legible figures at each3, for use in reading bearings by an azimuth circle or in laving the course to degrees.The card is provided with a concentric spheroidal air vessel, to buoy its ownweight and that of the magnets, allowing a pressure of between 60 and 90 grains onthe pivot at 60 F.; the weight of the card in air is 3,060 grains. The air vessel haswithin it a hollow cone, open at its lower end, and provided with the pivot bearingor cap, containing a sapphire, which rests upon the pivot and thus supports thecard; the cap is provided with adjusting screws for accurately centering the card.The pivot is fastened to the center of the bottom of the bowl by a flanged plate andscrews. Through this plate and the bottom of the bowl are two small holes whichcommunicate with the expansion chamber and admit of a circulation of the liquidbetween it and the bowl. The pivot is of gun metal with an iridium cap.The card is mounted in a bowl of cast bronze, the glass cover of which is closelypacked with rubber, preventing the evaporation or leakage of the liquid, which entirelynils the bowl. This liquid is composed of 45 per cent pure alcohol and 55 per centdistilled water, and remains liquid below 10 F.The lubber s line is a fine line drawn on an enameled plate on the inside of thebowl, the inner surface of the latter being covered with an insoluble white paint.Beneath the bowl is a metallic self-adjusting expansion chamber of elastic metal,by means of which the bowl is kept constantly full without the show of bubbles or thedevelopment of undue pressure caused by the change in volume of the liquid dueto changes of temperature.The rim of the compass bowl is made rigid and its outer edge turned strictlyto gauge to receive the azimuth circle.32. THE DRY COMPASS. The Lord Kelvin Compass, which may be regardedas the standard for the dry type, consists of a strong paper card with thecentral parts cut away and its outer edge stiffened by a thin aluminum ring. The

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20 INSTRUMENTS AND ACCESSORIES IN NAVIGATION.standard compass being located, all peloruses may be oriented from it by any oneof the following methods :

(a) By making the azimuth of a celestial body, taken by the pelorus, coincidewith the simultaneous azimuth of the same body taken by the standard compass.(b) By a similar process with distant objects; and the parallax may be entirelyeliminated in an apparently near object, in view of the moderate distance that

usually separates the two instruments on board ship.(c) By reciprocal bearings between the correct instrument and the instrumentto be established; it is evident that if the lubber lines of the two instruments areboth in the direction of the keel line, the bearing of the sight vane of each from theother (one being reversed) should coincide.(d) By computing the angle subtended at the pelorus by the fore-and-aft line

through the pelorus and the line drawn through the pelorus to the jack staff, andsetting the pelorus at this angle and sighting on the jack staff.

THE CHART.37. A nautical chart is a miniature representation upon a plane surface, inaccordance with a definite system of projection or development, 01 a portion of the

navigable waters of the world. It generally includes the outline of the adjacentland, together with the surface forms and artificial features that are useful as aidsto navigation, and sets forth the depths of water, especially in the near approachesto the land, by soundings that are fixed in position by accurate determinations.Except in charts of harbors or other localities so limited that the curvature of theearth is inappreciable on the scale of construction, a nautical chart is always framedover with a network of parallels of latitude and meridians of longitude in relationto which the features to be depicted on the chart are located and drawn; and themathematical relation between the meridians and parallels of the chart and thoseof the terrestrial sphere determines the method of measurement that is to be employedon the chart and the special uses to which it is adapted.38. There are three principal systems of projection in use: (a) the Mercator,(b) the polyconic, and (c) the gnomonic; of these theMercator is byfarthe most generallyused for purposes of navigation proper, while the polyconic and the gnomonic chartsare employed for nautical purposes in a more restricted manner, as for plottingsurveys or for facilitating great circle sailing.39. THE MERCATOR PROJECTION. The Mercator Projection, so called, may besaid to result from the development, upon a plane surface, of a cylinder which istangent to the earth at the equator, the various points of the earth s surface havingbeen projected upon the cylinder in such manner that the loxodromic curve orrhumb line (art. 6, Chap. I) appears as a right line preserving the same angle ofbearing with respect to the intersected meridians as does the ship s track.In order to realize this condition, the line of tangency, which coincides with theearth s equator, being the circumference of a right section of the cylinder, will appearas a right ^line on the development; while the series of elements of the cylindercorresponding to the projected terrestrial meridians will appear as equidistant rightlines, parallel to each other and perpendicular to the equator of the chart, maintaining the same relative positions and the same distance apart on that equator asthe meridians have on the terrestrial spheroid. The series of terrestrial parallelswill also appear as a system of right lines parallel to each other and to the equator,and will so^intersect the meridians as to form a system of rectangles whose altitudes,for successive intervals of latitude, must be variable, increasing from the equator insuch manner that the angles made by the rhumb line with the meridian on the chartmay maintain the required equality with the corresponding angles on the spheroid.

, 40. MERIDIONAL PARTS. At the equator a degree of longitude is equal to adegree of latitude^ but in receding from the equator and approaching the pole, whilethe degrees of latitude remain always of the same length (save for a slight changedue to the fact that the earth is not a perfect sphere), the degrees of longitude becomeless and less.Since, in the Mercator projection, the degrees of longitude are made to appeareverywhere of the same length, it becomes necessary, in order to preserve the propor-


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INSTRUMENTS AND ACCESSOKIES IN NAVIGATION. 21tion that exists at different parts of the earth s surface between degrees of latitudeand degrees of longitude, that the former be increased from their natural lengths,and such increase must become greater and greater the higher the latitude.The length of the meridian, as thus increased, between the equator and anygiven latitude, expressed in minutes at the equator as a unit, constitutes the numberof Meridional Parts corresponding to that latitude. The Table of Meridional Partsor Increased Latitudes (Table 3), computed for every minute of latitude betweenand 80, affords facilities for constructing charts on "the Mercator projection and forsolving problems in Mercator sailing.41. To CONSTRUCT A MERCATOR CHARTS If the chart for which a projectionis to be made includes the equator, the values to be measured off are given directlyby Table 3. If the equator does not come upon the chart, then the parallels oflatitude to be laid down should be referred to a principal parallel, preferably the lowestparallel to be drawTi on the chart. The distance of any other parallel of latitudefrom the principal parallel is then the difference of the values for the two taken fromTable 3.

The values so found may either be measured off, without previous numericalconversion, by means of a diagonal scale constructed on the chart, or they may belaid dowTi on the chart by means of any properly divided scale of yards, meters, feet,or miles, after having been reduced to the scale of proportions adopted for the chart.If, for example, it be required to construct a chart on a scale of one-quarter of aninch to five minutes of arc on the equator, a diagonal scale may first be constructed,on which ten meridional parts, or ten minutes of arc on the equator, have a lengthof half an inch.It may often be desirable to adapt the scale to a certain allotment of paper. Inthis case, the lowest and the highest parallels of latitude may first be drawn on thesheet on which the transfer is to be made. The distance oetween these parallelsmay then be measured, and the number of meridional parts between them ascertained.

Dividing the distance by this number will then give the length of one meridionalpart, or the quantity by which all the meridional parts taken from Table 3 must bemultiplied. This quantity will represent the scale of the chart. If it occurs that thelimits of longitude are a governing consideration, the case may be similarly treated.EXAMPLE: Let a projection be required for a chart of 14 extent in longitudebetween the parallels of latitude 20 30 and 30 25 , and let the space allowable onthe paper between these parallels measure 10 inches.Entering the column in Table 3 headed 20, and running down to the line marked30 in the side column, will be found 1248.9; then, entering the column 30, andrunning dowTi to the line 25 , will be found 1905.5. The difference, or 1905.51248.9 = 656.6, is the value of the meridional arc between these latitudes, for which1 of arc of the equator is taken as the unit. On the intended projection, therefore,

10inI 7 of arc of longitude will measure .,. =0.0152 inch, which will be the scale of theo5o.bchart. For the sake of brevity call it 0.015. By this quantity all the values derivedfrom Table 3 will have to be multiplied before laying them down on the projection, ifthey are to be measured on a diagonal scale of one inch.Draw in the center of the sheet a straight line, and assume it to be the middlemeridian of the chart. Construct very carefully on this line a perpendicular nearthe lower border of the sheet, and assume this perpendicular to be the parallel oflatitude 20 30 ; this will be the southern inner neat line of the chart. From theintersection of the lines lay off on the parallel, on each side of the middle meridian,seven degrees of longitude, or distances each equal to 0.015X60X7 = 6.3 inches;and through the points thus obtained draw lines parallel to the middle meridian,and these will be the eastern and western neat lines of the chart.In order to construct the parallel of latitude for 21 00 , find, in Table 3, themeridional parts for 21 00 , which are 1280.8. Subtracting from this number thenumber for 20 30 , and multiplying the difference by 0.015, we obtain 0.478 inch,which is the distance on the chart between 20 30 and 21 00 . On the meridians

a This construction for the purpose of plotting lines of position in ordinary navigation will often be unnecessary if use ismade of the Position Plotting Sheets published by the Hydrographic Office.


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20 INSTRUMENTS AND ACCESSORIES IN NAVIGATION.standard compass being located, all peloruses may be oriented from it by any oneof the following methods :

(a) By making the azimuth of a celestial body, taken by the pelorus, coincidewith the simultaneous azimuth of the same body taken by the standard compass.(&) By a similar process with distant objects; and the parallax may be entirelyeliminated in an apparently near object, in view of the moderate distance that

usually separates the two instruments on board ship.^(c) By reciprocal bearings between the correct instrument and the instrumentto be established; it is evident that if the lubber lines of the two instruments areboth in the direction of the keel line, the bearing of the sight vane of each from theother (one being reversed) should coincide.(d) By computing the angle subtended at the pelorus by the fore-and-aft line

through the pelorus and the line drawn through the pelorus to the jack staff, andsetting the pelorus at this angle and sighting on the jack staff.

THE CHART.37. A nautical chart is a miniature representation upon a plane surface, inaccordance with a definite system of projection or development, of a portion of the

navigable waters of the world. It generally includes the outline of the adjacentland, together with the surface forms and artificial features that are useful as aidsto navigation, and sets forth the depths of water, especially in the near approachesto the land, by soundings that are fixed in position by accurate determinations.Except in charts of harbors or other localities so limited that the curvature of theearth is inappreciable on the scale of construction, a nautical chart is always framedover with a network of parallels of latitude and meridians of longitude in relationto which the features to be depicted on the chart are located and drawn; and themathematical relation between the meridians and parallels of the chart and thoseof the terrestrial sphere determines the method of measurement that is to be employedon the chart and the special uses to which it is adapted.38. There are three principal systems of projection in use: (a) the Mercator,(&) the polyconic, and (c) the gnomonic; of these theMercator is byfarthe most generallyused for purposes of navigation proper, while the polyconic and the gnomonic chartsare employed for nautical purposes in a more restricted manner, as for plottingsurveys or for facilitating great circle sailing.39. THE MERCATOR PROJECTION. The Mercator Projection, so called, may besaid to result from the development, upon a plane surface, of a cylinder which istangent to the earth at the equator, the various points of the earth s surface havingbeen projected upon the cylinder in such manner that the loxodromic curve orrhumb line (art. 6, Chap. I) appears as a right line preserving the same angle ofbearing with respect to the intersected meridians as does the ship s track.In order to realize this condition, the line of tangency, which coincides with theearth s equator, being the circumference of a right section of the cylinder, will appearas a right line on the development; while the series of elements of the cylindercorresponding to the projected terrestrial meridians will appear as equidistant rightlines, parallel to each other and perpendicular to the equator of the chart, maintaining the same relative positions and the same distance apart on that equator asthe meridians have on the terrestrial spheroid. The series of terrestrial parallelswill also appear as a system of right lines parallel to each other and to the equator,and will so^intersect the meridians as to form a system of rectangles whose altitudes,for successive intervals of latitude, must be variable, increasing from the equator insuch manner that the angles made by the rhumb line with the meridian on the chartmay maintain the required equality with the corresponding angles on the spheroid.

, 40. MERIDIONAL PARTS. At the equator a degree of longitude is equal to adegree of latitude^ but in receding from the equator and approaching the pole, whilethe degrees of latitude remain always of the same length (save for a slight changedue to the fact that the earth is not a perfect sphere), the degrees of longitude becomeless and less.Since, in the Mercator projection, the degrees of longitude are made to appeareverywhere of the same length, it becomes necessary, in order to preserve the propor-


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22 INSTRUMENTS AND ACCESSORIES IN NAVIGATION.lay off distances equal to 0.478 inch, and through the three points thus obtaineddraw a straight line, which will be the parallel of 21 00 .Proceed in the same manner to lay down all the parallels answering to fulldegrees of latitude; the distances will be respectively:

Oin.015X (1344.9- 1248.9) = 1.440 inches.Oin.015 X (1409.5 - 1248.9) = 2.409 inches.Oin . 105 X (1474.5 -1248.9) =3.384 inches, etc.

Thus will be shown the parallels of latitude 22 00 , 23 0 sin 2^+E cos 2z r ,where d is the deviation, and z the ship s heading by compass, measured fromcompass North.

115. MEAN DIRECTIVE FORCE. The effect of the disturbing forces isnot confinedto causing deviations ; it is only those components acting at right angles to the needlewhich operate to produce deflection; the effect of those acting in the direction ofthe needle is exerted either in increasing or diminishing the directive force of thecompass, according as the resolved component is northerly or southerly.It occurs, with the usual arrangement of iron in a vessel, that the mean effectof this action throughout a complete swing of the ship upon all headings is to reducethe directive force that is, while it varies with the heading, the average value uponall azimuths is minus or southerly. The result of such a condition is unfavorablefrom the fact that the compass is thus made more " sluggish," is easily disturbedand does not return quickly to rest, and a given deflecting force produces a greaterdeviation when the directive force is reduced. The usual methods of compensationlargely correct this fault, but do not entirely do so ; it is therefore the case that themean combined horizontal force of earth and ship to north is generally less than thehorizontal force of the earth alone; but it is only in extreme cases that this deficiencyis serious.116. HEELING ERROR. This is an additional cause of deviation that ariseswhen the vessel heels to one side or the other. Heretofore only those forces havebeen considered which act when the vessel is on an even keel; but if there is an inclination from the vertical certain new forces arise, and others previously inoperativebecome effective. These forces are (a) the vertical component of the subpermanentmagnetism acquired in building; (b) the vertical component of the induced magnetismin vertical soft iron, and (c) the magnetism induced by the vertical component ofthe earth s total force in iron which, on an even keel, was horizontal. The first twoof these disturbing causes are always present, but, when the ship is upright, have notendency to produce deviation, simply exerting a downward pull on one of the polesof the needle; the last is a new force that arises when the vessel heels.The maximum disturbance due to heel occurs when the ship heads North orSouth. When heading East or West there will be no deviation produced, althoughthe directive force of the needle will be increased or diminished. The error willincrease with the amount of inclination from the vertical.

117. For the same reason as was explained in connection with semicirculardeviations, that part of the heeling error due to subpermanent magnetism will vary,on change of latitude, as YJ> while that due to vertical induction will vary as tan 0.In south magnetic latitude the effect of vertical induction will be opposite in directionto what it is in north latitude.118. The heeling error is corrected by a permanent magnet placed in a verticalposition directly under the center of the compass. Such a magnet has no effect uponthe compass when the ship is upright ; but since its force acts in an opposite directionto the force of the ship which causes heeling error, is equal to the latter in amount,and is exerted under the same conditions, it affords an effective compensation. Forsimilar reasons to those affecting the compensation of B and C, the correction bymeans of a permanent magnet is not general and must be rectified upon change oflatitude. PRACTICAL COMPENSATION.

119. In the course of explanation of the different classes of deviation occasionhas been taken to state generally the various methods of compensating the errors thatare produced. The practical methods of applying the correctors wiu next be given.120. ORDER OF CORRECTION. The following is the order of steps to be followedin each case. It is assumed that the vessel is on an even keel, that the compass isproperly centered in the binnacle, that all surrounding masses of iron or steel are intheir normal positions, all correctors removed, and that the binnacle is one in which

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50 THE COMPASS EBROB.the semicircular deviation is corrected by two sets of permanent magnets at rightangles to each other.In order to ascertain if the compass is properly centered in the binnacle, theheeling corrector may be temporarily placed in its tube and drawn from its lowestto its nighest position; if no deflection is shown by the needle the compass is properly centered; if not it should be adjusted by the screws provided for the purpose.

1 . Place quadrantal correctors by estimate.2. Correct semicircular deviation.3. Correct quadrantal deviation. _4. Swin^ ship for residual deviations.The heeling corrector may be placed at any time after the semicircular and

quadrantal errors are corrected. A Flinders bar can be put in place only afterobservations in two latitudes.121. The ship is first placed on some magnetic cardinal point. If North orSouth, the only force (theoretically speaking) which tends to produce deflection of theneedle will be the athwartship component of the semicircular force, whose effect isrepresented by the coefficient C. It East or West, the only deflecting force will bethe fore-and-aft component of the semicircular force, whose effect is represented bythe coefficient B. This will be apparent from a consideration of the direction of theforces producing deviation, and is also shown by the equation connecting the terms(where A and E are zero) :

d = B sin z f + C cos z + D sin 2z .If the ship is headed North or South, z being equal to or 180, the equationbecomes d = C. If on East or West, z being 9(T or 270, we have d = B.This statement is exact if we regard only the forces that have been consideredin the problem, but experience has demonstrated that the various correctors whenin place create certain additional forces by their mutual action, and in order to correct

the disturbances thus accidentally produced, as well as those due to regular causes,it is necessary that the magnetic conditions during correction shall approximate asclosely as possible to those that exist when the compensation is completed; thereforethe quadrantal correctors should first be placed on their arms at the positions whichit is estimated that they will occupy later when exactly located. An error in theestimate will have but slight effect under ordinary conditions. It should be understood that the placing of these correctors has no corrective effect while the ship is ona cardinal point. Its object is to create at once the magnetic field with which weshall have to deal when compensation is perfected.This having been done, proceed to correct the semicircular deviation. If theship heads North or South, the force producing deflection is, as has been stated, theathwartship component of the semicircular force, which is to be corrected by permanent magnets placed athwartships ; therefore enter in the binnacle one or more suchmagnets, and so adjust their height that the heading of the ship by compass shallagree with the magnetic heading. When this is done all the deviation on thatazimuth will be corrected.

Similarly, if the ship heads East or West, the force producing deviation is thefore-and-aft component of the semicircular force, and this is to be corrected byentering fore-and-aft permanent magnets in the binnacle and adjusting the heightso that the deviation on that heading disappears.With the deviation on two adjacent cardinal points corrected, the semicircularforce has been completely compensated. Next correct the quadrantal deviation.Head the ship NE., SE., SW., or NW. The coefficients B and C having been reducedto zero by compensation, and 2z f , on the azimuths named, being equal to 90 or 270,the equation becomes d = D. The soft-iron correctors are moved in or out fromthe positions in which they were placed by estimate until the deviation on the heading(all of which is due to quadrantal force) disappears. The quadrantal disturbingforce is then compensated.122. DETERMINATION OF MAGNETIC HEADINGS. To determine when a shipis heading on any given magnetic course, and thus to know when the deviation hasbeen corrected and the correctors are in proper position, four methods are available:


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THE COMPASS ERROR. 51(a) Swing the ship and obtain by the best available method the deviations on a

sufficient number of compass courses to construct a curve on the Napier diagramfor one quadrant, and thus find the compass headings corresponding to two adjacentmagnetic cardinal points and the intermediate intercardinal point, as North, NE.,and East, magnetic. Then put the ship successively on these courses, noting thecorresponding headings by some other compass, and when it is desired to head onthe various magnetic azimuths during the process of correction the ship may besteadied upon them by the auxiliary compass. Variations of this method will suggestthemselves and circumstances may render their adoption convenient. The compasscourses corresponding to the magnetic directions may be obtained from observationsmade with the auxiliary compass itself, or while making observations with anothercompass the headings by the auxiliary may be noted and a curve for the latterconstructed, as explained in article 95, and the required headings thus deduced.

(6) By the methods to be explained hereafter (Chap. XIV), ascertain in advancethe true bearing of the sun at frequent intervals during the period which is to bedevoted to the compensation of the compasses; apply to these the variation andobtain the magnetic bearings ; record the times and bearings in a convenient tabularform, or, better still, plot a curve of magnetic azimuths of the sun on cross section paper,thecoordinates being local apparent time and magnetic bearings of the sun, as describedin article 89. Set the watch accurately for the local apparent time; then when itis required to steer any given magnetic course, set that point of the pelorus for theship s head and set the sight vanes for the magnetic bearing of the sun correspondingto the time by watch. Maneuver the ship with the helm until the sun comes on thesight vanes, when the azimuth of the ship s head will be that which is required. Thesight vanes must be altered at intervals to accord with the curve or table of timesand bearings.

(c) Construct a curve or table showing times and corresponding magneticbearings of the sun, and also set the watch, as explained for the previous method.Then place the sight vanes of the azimuth circle of the compass at the proper angulardistance to the right or left of the required azimuth of the ship s head ; leave them soset and maneuver the ship with the helm until the image of the sun comes on withthe vanes. The course will then be the required one. As an example, suppose thatthe curve or table shows that the magnetic azimuth of the sun at the time given bythe watch is N. 87 E., and let it be required to head magnetic North; when placedupon this heading, therefore, the sun must bear 87 to the right or east of thedirection of the ship s head; when steady on any course, turn the sight vane to therequired bearing relative to the keel. It on N. 11 W., for example, turn the circleto N. 76 E.; leave the vane undisturbed and alter course until the sun comes on.The magnetic heading is then North, and adjustment may be made accordingly.(d) When ranges are available, they may be utilized for determining magneticheadings.123. SUMMARY OF ORDINARY CORRECTIONS. To summarize, the following isthe process of correcting a compass for a single latitude, where magnets at rightangles are employed for compensating the semicircular deviation and where the disturbances due to unsymmetrical soft iron are small enough to be neglected.First. All correctors being clear of the compass, place the quadrantal correctorsin the position which it is estimated that they will occupy when adjustment is complete. The navigator s experience will serve in making the estimate, or if thereseems no other means of arriving at the probable position they may be placed at themiddle points of their supports.Second. Steady the ship on magnetic north, east, south, or west, and hold onthat heading by such method as seems best. By means of permanent magnets alterthe indications of the compass until the heading coincides with the magnetic course.If heading north, magnets must be entered north ends to starboard to correct easterlydeviation and to port to correct westerly, and the reverse if heading south. Ifheading east, enter north ends forward for easterly and aft for westerly deviations,and the reverse if heading west. (Binnacles differ so widely in the methods of carrying magnets that details on this point are omitted. It may be said, however, that

o This is all that is required for the purposes of compensation, but if there is opportunity it is always well to make a completeswing and obtain a full table of deviations, which may give interesting information of the existing magnetic conditions.


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54 THE COMPASS ERROR.It should be noted, however, that it is extremely difficult to get soft iron rodsof a satisfactory quality, for, after being placed, they seldom fail to take up moreor less subpermanent magnetism. This magnetism, due to shock of gunfire, vibration while cruising or on speed trials, etc., is subject to greater and more erraticchanges than that of the harder portion of the hull, and its proximity to the compassintensifies the effect of the variations in its magnetic properties.127. When it is not possible to correct the compass at the magnetic equatorthere is no ready practical method by which the Flinders bar may be placed; theoperation will then depend entirely upon computation, and as a mathematical

analysis of deviations is beyond the scope laid out for this work the details of procedure will not be gone into; the general principles involved are indicated, andstudents seeking more must consult the various works that treat the subject fully.It has been explained that each coefficient of semicircular deviation (B and C)is made up of a subpermanent factor varying as jj and of a vertical induction factorvarying as tan 0. If we indicate by the subscripts s and v , respectively, the parts dueto each force, we may write the equations of the coefficients:

; and

tr-v tan d.Now if we distinguish by the subscripts 1 and 2 the values in the first and in thesecond position of observation, respectively, of those quantities that vary with themagnetic latitude, we have :

B. X TT-+BV X tan #!,**tand

C2 = C8 X TT-+ Cv X tan 2 .-ti2The values of the coefficients in both latitudes are found from the observationsmade for deviations; the values of the horizontal force and of the dip at each placeare known from magnetic charts; hence we may solve the first pair of equations forB8 and Bv , and the second pair for C8 and Cv ; and having found the values of thesevarious coefficients, we may correct the effects of Bs and C3 by permanent magnetsin the usual way and correct the remainder that due to Bv and Cv by the Flindersbar.Strictly, the Flinders bar should be so placed that its repelling pole is at an

angular distance from ahead equal to the "starboard angle" of the attracting poleof the vertical induced force, this angle depending upon the coefficients Bv and Cv ;but since, as before stated, horizontal soft iron may usually be regarded as symmetrical, Cv is assumed as zero and the bar placed in the midship line.128. To CORRECT ADJUSTMENT ON CHANGE OF LATITUDE. The compensationof quadrantal deviation, once properly made, remains effective in all latitudes, excepting as noted in article 110; but unless a Flinders bar is used a correction of thesemicircular deviation made in one latitude will not remain accurate when thevessel has materially changed her position on the earth s surface. With this inmind the navigator must make frequent observations of the compass error duringa passage and must expect that the table of residual deviations obtained in themagnetic latitude of compensation will undergo considerable change as that latitude


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THE COMPASS EKKOB. 55is departed from. The new deviations may become so large that it will be foundconvenient to readjust the semicircular correcting magnets. This process is verysimple.

)he athwartship magnets or alter their number until the deviation disappears; thonsteady on East or West (magnetic) and similarly adjust the fore-and-aft magnets,Swing ship for a new table of residual deviations.129. It must be borne in mind that the compensation of the compass is notan exact science and that the only safeguard is unceasing watchfulness on the navigator s part. As the ship s iron is partly "hard" and partly "soft," the subper-manent magnetism may change appreciably from day to day, especially in a newship as the magnetism absorbed in building "shakes out." After a ship has been inservice for one or two years, the magnetic conditions may be said to be "settled."They undergo changes, however, to a greater or less extent, on account of the following influences or conditions:

(a) Continuous steaming on one general course for several days, especially inrough weather, or lying alongside a dock on one heading for a long period.

(b) Shock of gunfire, even on a ship that has been in commission for more thana year, has been Known to introduce an 8 error, which disappeared in the course ofa few days.(c) Extensive alterations or repairs in the vicinity of the compass. The use of

scaling hammers on a military top caused a 3 change in one of the U. S. S. 6V/-necticut s compasses.(d) Steaming with boilers (especially under forced draft) whose funnel is nearthe compass has been known to cause a change of more than 10, the retained magnetism being "cooked out."(e) On the U. S. S. Oregon, a grounded searchlight circuit caused a change of 9.(/) Ships have reported changes of as much as 7 when struck by lightning orafter passing through very severe thunderstorms.The binnacle fittings must be carefully inspected from time to time, to see thatthe correctors have not changed position. At least once a year the quadrantalcorrectors should be examined for polarity. This can be done by moving them,one at a time, as close to the compass as practicable and then revolving them slowlyabout the vertical axis; if the compass is deflected, the magnetism should be removedby bringing the sphere to a low red heat and then letting it cool slowly.Tliere is no excuse for large deviations in a standard or steering compass, and theyshould not le allowed to exist.


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CHAPTER IV.PILOTING,

130. Piloting, in the sense given the word by modern and popular usage, is the; rt of conducting a vessel in channels and harbors and along coasts, where landmarks,;nd aids to navigation are available for fixing the position, and where the depth ofv/ater and dangers to navigation are such as to require a constant watch to be keptupon the vessel s course and frequent changes to be made therein.

Piloting is the most important part of navigation and the part requiring the mostt xperience and nicest judgment. An error in position on the high seas may be rectifiedby later observation, but an error in position while piloting usually results in disaster.Therefore the navigator should make every effort to be proficient in this importantbranch, bearing in mind that a modern vessel is usually safe on the high seas and indanger when approaching the land and making the harbor.131. Requisites. The navigator should have ready on approaching the landthe charts of the coast and the largest scale detail charts of the locality at which hexpects to make his landfall, the sailing directions, and the light and buoy list, allCorrected for the latest information from the Notices to Mariners and other sources.The usual instruments employed in navigation should be at hand and in good workingrder. The most important instrument the sounding machine should be in placeand in order at least a day before the land is to be made. The importance of thesounding machine can not be exaggerated. The latest deviation table for the standardcompass must be at hand.132. LAYING THE COURSE. Mark a point upon the chart at the ship s position;then mark another point for which it is desired to steer; join the two by a line drawnv/ith the parallel ruler, and, maintaining the direction of the line, move the ruleruntil its edge passes through the center of the compass rose and note the direction.f the compass rose indicates Redirections, this will be the true course; and must beorrected for variation and deviation (by applying each in the opposite directiono its name) to obtain the compass course; ii it is a magnetic rose, the course neede corrected for deviation only.Before putting the ship on any course a careful look should be taken along theline over which it leads to be assured that it clears all dangers.133. METHODS OF FIXING POSITION. A navigator in sight of objects whosepositions are shown upon the chart may locate his vessel by any one of the followinglethods: ^(a) cross bearings of two known objects; (b) the bearing and distance of anown object; (c) the bearing of a known object and the angle between two knownbjects; (d) two bearings of a known object separated by an interval of time, withh.e^run during that interval; (e) sextant angles between three known objects.Besides the foregoing there are two methods by which, without obtaining the precise

^osition, the navigator may assure himself that he is clear of any particular danger.These are: (f) the danger angle ; (#) the danger bearing.^The choice of the method will be governed by circumstances, depending uponwhich is best adapted to prevailing conditions.

^134. CROSS BEARINGS OF Two KNOWN OBJECTS. Choose two objects whose

position on the chart can be unmistakably identified and whose respective bearingsi rom the ship differ, as nearly as possible by 90; observe the bearing of each, eitherby compass or pelorus, taking one as quickly as possible after the other; see thatthe ship is on an even keel at the time the observation is made, and, if using thepelorus, be sure also that she heads exactly on the course for which the pelorus is set.Correct the bearings so that they will be either true or magnetic, according as they areto be plotted by the true or magnetic compass rose of the chart that is, if observedby compass, apply deviation and variation to obtain the true bearing, or deviation56


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PILOTING. 57only to obtain the magnetic; if observed by pelorus, that instrument should be setfor the true or magnetic heading, according as one or the other sort of reading isrequired, and no further correction will be necessary. Draw on the chart, by meansof the parallel rulers, lines which shall pass through the respective objects in thedirection that each was observed to bear. As the ship s position on the chart isknown to be at some point of each of these lines, it must be at their intersection, theonly point that fulfills both conditions.In figure 13, if A and B are the objects and OA and OB the lines passing throughthem in the observed directions, the ship s position will be at O, their intersection.The plotting of a position from two bearings is

greatly facilitated by the use of a plotter devised byLieut. K. A. Koch, United States Navy, as reference tothe compass rose on the chart, the use of parallel rulers,and the drawing of lines on the chart are obviated. Abrief description of this plotter and its uses is as follows:All materials except bolt and washers are transparent.A square (7 by 7 inches) ruled with two series of linesat right angles about one-half inch apart, and a disk(7J inches in diameter) marked in degrees are placedon a central hollow bolt of brass and are capable ofbeing clamped together with any degree of friction required. Three arms are placed so as to revolve aroundthe same hollow bolt and can be clamped together inany position. In order to plot a position from compassbearings of two objects, and lay off a new course, the FIG. 13.zero mark of the disk should be revolved to the Eastor West of the true North and South line of the square by an amount equal to thecompass error in degrees. Two of the arms are then set by the degrees on thedisk to the two observed compass bearings. The plotter is then manipulated on thechart until the two arms intersect the objects observed and the vertical lines on thesquare are parallel to the meridians of the chart. Mark the point of intersection ofthe arms by inserting a pencil in the hollow central bolt. An arm may then be swungto intersect any object 011 the chart and the compass course to that object read fromthe disk. This plotter can also be used to obtain the error of the compass frombearings of three objects by compass.135. If it be possible to avoid it, objects should not be selected for crossbearings which subtend an angle at the ship of less than 30 or more than 150, as,when the lines of bearing approach parallelism, a small error in an observed bearinggives a large error in the result. For a similar reason objects near the ship should betaken in preference to those at a distance.136. When a third object is available a bearing of that may be taken and plotted.If this line intersects at the same point as the other two (as the bearing OC of theobject C in the figure), the navigator may have a reasonable assurance that his "fix"is correct; if it does not, it indicates an error somewhere, and it may have arisen frominaccurate observation, incorrect determination or application of the deviation, or afault in the chart.

137. What may be considered as a form of this method can be used when onlyone known object is in sight by taking, at the same instant as the bearing, an altitudeof the sun or other heavenly body and noting thetune; work out the sight and obtain the Sumnerline (as explained in Chapter XV), and the intersection of this with the direction line from theobject will give the observer s position in the same X)way as from two terrestrial bearings.138. BEARING AND DISTANCE OF A KNOWNOBJECT. When only one object is available, theship s position may be found by observing its bearing and distance. Follow the preceding method in FlG. 14>the manner of taking, correcting, and plotting thebearing; then, on this line, lay off the distance from the object, which will give tpoint occupied by the observer. In figure 14, if A represents the object and AO:ing and distance, the position sought will be at O.arn


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60 PILOTING.EXAMPLE: A vessel on a course 128 takes the first bearing of an object at154, and the second at 182, running in the interval 0.8 mile. Required the distanceat which she will pass abeam.Difference between course and first bearing, 26Difference between course and second bearing, 54.

Multiplier from second column, Table 5B, 0.76.0. 8 mile X 0.76 = 0. 6 mile, distance of passing abeam.145. As has been said, there are certain special cases ot this problem where it is

exceptionally easy of application; these arise when the multiplier is equal to unityand the distance run is therefore equal to the distance fromthe object. When the angular distance on the bow at thesecond bearing is twice as great as it was at the first bearing,the distance of the object from the ship at second bearing isequal to the run, the multiplier being 1.0. For if, in figure 18,when the ship is in the first position, O, the object A bears aon the bow, and at the second position, P, 2a, we have in thetriangle APO, observing that APO = 180 - 2o?, and POA= a :

PAO = 180- (POA+APO),a.

FIG. 18.

Or, since the angles at O and A are equal to each other, the sidesOP and AP are equal or the distance at second bearing is equalto the run. This is known as doubling the angle on the low.146. A case where this holds good is familiar to everynavigator as the ~bow and beam bearing, where the first bearingis taken when the object is broad on the bow (four points or45 from ahead) and the second when it is abeam (eight points or 90 from ahead);in that case the distance at second bearing and the distance abeam are identicaland equal to the run between bearings.147. When the first bearing is 26J from ahead, and the second 45, the distanceat which the object will be passed abeam will equal the run between bearings. This

is true of any two such bearings whose^ natural cotangents ^ differ by unity, andthe following table is a collection of solutions of this relation in which the pairs ofbearings are such that, when observed in succession from ahead upon the same fixedobject, the distance run between the bearings will be equal to the distance of the fixedobject when it bears abeam, provided that a steady course has been steered, unaffectedby current or drift.The marked pairs will probably be found the most convenient ones to use, asthey involve whole degrees only.

Bearingsfrom ahead.

When the fixed object bears as per any entry of the first column, take the timeand the reading of the patent log. Repeat this procedure on reaching the bearing ofthe adjacent entry in the second column. The difference of the patent-log readingswill be the distance at which the fixed object will be passed abeam.


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PILOTING. 61This general solution includes the 26-45 rule as well as the seven-tenths ruleto be explained later; furthermore, it has the advantage that the approximatedetermination of the distance offshore, at which the fixed object will be passed,need not wait for the 45 bearing. There are two whole-degree pairs bv which sucha determination can be made before the 45 bearing is reached. It is possible to

get five whole-degree bearings or observations by the time the fixed object bears 30forward of the beam, as follows: 22-34, 25-41, 27-46, 29-51, 32-59. Ofthese, the last three should be reasonably accurate; the acuteness of the first anglein all such observations accounts for the discrepancies noted in practice. The useof the table given above may be found to be more convenient than the methods ofplotting about to be described, and the use of tables 5A and 5B; but it does not takethe place of those methods. Tables 5A and 5B coyer all combinations of bearings inwhich the first bearing is taken when the object is 20 or more on the bow.The Seven-tenths Rule. If bearings of the fixed object be taken at two (2)and four (4) points on the bow (22J and 45), seven-tenths (0.7) of the run between"bearings will be the distance at which the point will be passed abeam.From the combination of the seven-tenths rule and the 26^-45 rule, therefollows an interesting corollary, i. e., if bearings of an object at 22^ and 26^ on thebow be taken, then seven-thirds (J) of the distance run in the interval will be thedistance when abeam.

If a bearing is taken when an object is two points (22 ) forward of the beamand the run until it bears abeam is measured, then its distance when abeam is seven-thirds (-J) of the run. This rule, particularly, is only approximate.In case the 45 bearing on the bow is lost, in order to find the distance abeamthat the object is passed, note the time when the object bears 26^ forward of thebeam, and again when it has the same bearing abaft the beam; the distance run inthis interval is the distance of the object when it was abeam.

To steer an arc course in order to round a light, point, or other object withoutfixes and be sure the course itself does not decrease the initial distance: Providedthere is no current, stand on course until the light is at the required distance, determined by one or more of the methods described. Immediately bring the lightabeam, and dp not let it get forward of the beam again, then the course wih notdecrease the initial distance. When the light is onerhalf point abaft the beamagain bring it abeam; hold course until it is againone-half point abaft the beam, repeating this procedure until the light is rounded. A polygon is thuscircumscribed about the circle, the nearest approachto the light being the radius of the inscribed circle.The number of sides of the polygon may be increased indefinitely, so that the light may be rounded,by changing the course just enough to keep the lightabeam, after it is Jirst brought abeam.148. There is a graphic method of solving thisproblem that is considered by some more convenientthan^the use of multipliers. Draw upon the chartthe lines OA and PA (fig. 19), passing through theobject on the two observed bearings; set the dividersto the distance run, OP; lay down the parallel rulersin a direction parallel to the course and move themtoward or away from the observed object until somepoint is found where the distance between the linesof bearing is exactly equal to the distance betweenthe points of the dividers; in the figure this occurswhen the rulers lie along the line OP, and therefore O represents the position ofthe ship at the first bearing and P at the second. For any other positions O P ,O"P", the condition is not fulfilled.149. Another graphic solution is given by the Mooring and Maneuvering Boardand the various moclificatlons of it that are in use among navigators.150. The method of obtaining position by two bearings of the same object isone of great value, by reason of the fact that it is frequently necessary to locate theship when there is but one landmark in sight. Careful navigators seldom, if ever,

FIG. 19.


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60 PILOTING.EXAMPLE: A vessel on a course 128 takes the first bearing of an object at154, and the second at 182, running in the interval 0.8 mile. Required the distanceat which she will pass abeam.Difference between course and first bearing, 26Difference between course and second bearing, 54.

Multiplier from second column, Table 5B, 0.76.0. 8 mile X 0.76 = 0. 6 mile, distance of passing abeam.145. As has been said, there are certain special cases ot this problem where it is

exceptionally easy of application; these arise when the multiplier is equal to unityand the distance run is therefore equal to the distance fromthe object. When the angular distance on the bow at thesecond bearing is twice as great as it was at the first bearing,the distance of the object from the ship at second bearing isequal to the run, the multiplier being 1.0. For if, in figure 18,when the ship is in the first position, O, the object A bears aon the bow, and at the second position, P, 2a, we have in thetriangle APO, observing that APO = 180 - 2a, and POA a:

PAO = 180-(POA+ APO),

FIG. 18.

Or, since the angles at O and A are equal to each other, the sidesOP and AP are equal or the distance at second bearing is equalto the run. This is known as doubling the angle on the bow.146. A case where this holds good is familiar to everynavigator as the "bow and beam bearing, where the first bearingis taKen when the object is broad on the bow (four points or45 from ahead) and the second when it is abeam (eight points or 90 from ahead) ;in that case the distance at second bearing and the distance abeam are identicaland equal to the run between bearings.147. When the first bearing is 26^ from ahead, and the second 45, the distanceat which the object will be passed abeam will equal the run between bearings. This

is true of any two such bearings whose natural cotangents differ by unity, andthe following table is a collection of solutions of this relation in which the pairs ofbearings are such that, when observed in succession from ahead upon the same fixedobject, the distance run between the bearings will be equal to the distance of the fixedobject when it bears abeam, provided that a steady course has been steered, unaffectedby current or drift.The marked pairs will probably be found the most convenient ones to use, asthey involve whole degrees only.

Bearingsfrom ahead.

When the fixed object bears as per any entry of the first column, take the timeand the reading of the patent log. Kepeat this procedure on reaching the bearing ofthe adjacent entry in the second column. The difference of the patent-log readingswill be the distance at which the fixed object will be passed abeam.


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62 PILOTING.miss the opportunity for a bow and beam bearing in passing a lighthouse or otherwell-plotted object; it involves little or no trouble, and always gives a feeling ofaddea security, however little the position may be in doubt. If about to pass anobject abreast of which there is a danger a familiar example of which is when alighthouse marks a point off which are rocks or shoals a good assurance of clearanceshould be obtained before bringing it abeam, either by doubling the angle on thebow, or, if the object be sighted in time, by using any of the pairs of bearings tabulatedunder article 147.151. It must be remembered that, however convenient, the fix obtained bytwo bearings of the same object will be in error unless the course and distance arecorrectly estimated, the course "made good" and the distance "over the ground"being required. Difficulty will occur in estimating the exact course when there isbad steering, a cross current, or when a ship is making leeway; errors in the allowedrun will arise when she is being set ahead or back by a current or when the loggingis inaccurate. A current directly with the course of the ship, if unallowed for, willgive a determination of position too close to the object observed; and a current*directly against the course of the ship, if unallowed for, will give a determination ofposition too far away from the object observed. The existence of such a currentwill not le revealed by taking more than two successive bearings. All such observations will place the ship on the same apparent course, which course will be parallelto the course made good and to the course steered but in error in its distance fromthe observed object by an amount dependent upon the ratio of the speed of shipover ground to the speed of ship by log. A current oblique to the course of the shipwill give a determination of position which will be erroneous. The existence ofsuch a current but not its amount will "be revealed by taking more than two observations; in this case, following the usual method of plotting, the determination resultingfrom any two successive bearings will fail to agree with the determination from anyother two. If, in such a case, the observed bearings be drawn upon the chart andthe distances run by log between them be laid down on the scale of the chart upon apiece of paper, a course may be found by trial, upon which course the intervals ofrun correspond with the intervals between the lines of bearing. The apparent coursethus determined, which must always be oblique to the course steered, will be parallelto the course actually being made good, but will be in error in its distance from theobserved object by an amount dependent upon the ratio of the speed of ship overthe ground to the" speed of ship by log. If there is an apparant shortening of thedistance run from earlier to later observations, or a shortening of the time if thespeed is invariable, there is a component of set toward the fixed object. Therefore,if in a current of any sort, due allowance must be made, and it should be rememberedthat more dependence can be placed upon a position fixed by simultaneous bearingsor angles, when two or more objects are available, than by two bearings of a singleobject.152. SEXTANT A

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